Re: Linear operators 3

On Sep 23, 1:05 pm, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <1190529421.872576.145...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

jennifer <scrilla_12_1...@xxxxxxxxx> wrote:

[...]



But how do you ?

(i) Say how you "add" two elements of C^1([0,1]), and show that the
result will be in C^1([0,1]);
(ii) Say how you "multiply" an element of C^1([0,1]) by a scalar,
and show the result will be in C^1([0,1]);
(iii) Then show that, with those definitions of vector addition and
scalar multiplication, C^1([0,1])

Do you know any way by which, given a CONTINUOUS function f, you can

obtain a function F such that F' = f?

Fundamental theorem of Calculus!!!

Define addition in C^1([0,1]) by: (f+g)' = f' +g ' for f,g in
C^1([0,1])

NO. NO. NO. NO. NO.

Why are you differentiating? WHY?

THINK!!!!

You are given TWO FUNCTIONS f and g, with domain [0,1], and codomain
the real numbers; they are each differntiable, and both f' and g' are
continuous.

You want to ADD f AND g. You don't want to differentiate. You want to
add f and g to get a THIRD function, h, whose domain is also [0,1],
whose codomain is the real numbers; and then you want to show that h
will be differentiable and that h' will be continuous. ->THAT'S<- when
you are going to use derivatives; to check that your proposed h also
lies in C^1([0,1]). But you don't use derivatives to define the SUM OF
FUNCTIONS.

(af)' = af' for a in F, was a typo previously

Once again, I strongly urge you to drop this course. It is clear that
you are not ready for it.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

Sorry to dissapoint you but I will never quit,not like YOU, but i
would recommend you quit giving me a hard time and quit your position
at the University as I am sure that you have a lot of students who
think you are an arrogant and not exactly the best Lecturer out their.

Oh did i forget something, no!!!! you don't deserve to be called a
professor.

.

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